Patel became the second cabinet minister to quit in a week after admitting Wednesday her actions had "fallen below the high standards" required by her post.
Those actions included secret meetings with Israeli officials, among them Prime Minister Benjamin Netanyahu, without the government's knowledge.
The development comes seven days after former defense secretary Michael Fallon resigned over accusations of sexual impropriety. He, too, admitted his actions were less than exemplary.
May on Thursday promoted junior minister Penny Mordaunt to replace Patel, thus avoiding a major reshuffle.
Bad timing Brexit-wise
The timing couldn't have been worse for May as she resumes Brexit talks on Thursday.
"It’s obviously something that the government is not going to be very pleased about," Jeremy Stubbs, chairman of British Conservatives in Paris, told RFI.
"It cannot be said to strengthen the government, more likely to weaken it, but I don’t see what impact it could possibly have on the talks."
Nonetheless, Patel's departure deprives May of a keen Brexit campaigner and could undermine the prime minister's credibility when she faces the complicated task of unravelling more than 40 years of ties with the European Union.
"It’s true that Priti Patel was a keen Brexiteer and she’ll remain as such," comments Stubbs. "But whether she is in the government or on the back benches is not going to have any effect on these negotiations."
Not everyone agrees.
"It causes a deadlock in the negotiations," reckons Miroslav Poche, a Czech MEP with the Social Democratic Party in Prague.
"Because we can't understand British negotiators. And for EU diplomats and Members of Parliament and of the Commission team it's very difficult to negotiate with a weak British government."
In a week of crises Theresa May's foreign minister, Boris Johnson, was forced to apologise over remarks he made about a British-Iranian woman serving a five-year jail sentence in Iran.
Her family said Johnson's statement could harm her legal case.
"The weakness has allowed ministers to feel that they can go off and pursue independent policy," Tony Travers, director of the Institute of Public Affairs at the London School of Economics told RFI.
"Priti Patel and Boris Johnson are to name but two. The notion of collective cabinet responsibility, which is an essential part of the British executive functioning, has become, if not redundant, to some extent missing."
Growth blow to UK
And all of this is bad news for Brexit.
EU chief negotiator Michel Barnier has already warned that talks are in deadlock, partly over the divorce bill-- the amount of money the UK needs to pay to exit the EU--and partly over the issues of EU citizens' rights and the UK's land border with Ireland.
On Thursday the European Commission forecast eurozone growth at two percent in 2017 but reduced its estimate for the UK to 1.5 percent.
Czech MEP Poche even thinks there could be no Brexit at all.
"This is yet another example of what British people are starting to realise - Brexit is a bad solution," he says. "And I personally believe that there will be no Brexit after all because citizens are slowly learning what the EU really means for them and for the UK, so there is a growing possibility of new elections followed by a referendum."
But Theresa May's weakness, which is compounded by the catastrophe of June's general election, may also be her strength, Travers reckons.
"In a sense her weakness is the only thing that is keeping her there," he comments.
"One thing all Conservatives agree, one thing that binds them is the realisation that if they accidentally trigger another general election that would almost certainly produce a Labour government of some kind and they're very fearful of that."
The Tories loathe the prospect of a government under Labour's left-wing leader Jeremy Corbyn, he says.
Theresa May may be able to hang on to office, but in Europe patience is running out. EU leaders next meet in December, by then they'll be hoping there is some agreement on Brexit before they can move on to discussing trade.